Since this is your first year as an LLC, you might want to seek professional tax guidance.
For the period of September 1 to December 31, estimated taxes are due January 15 of the following year (in this instance January 17, 2022).
See https://www.irs.gov/payments/pay-as-you-go-so-you-wont-owe-a-guide-to-withholding-estimated-taxes-an...
There are no implications for deducting expenses. You can deduct expenses irrespective of whether or not estimated taxes are paid.
TurboTax will prepare Form 1040-ES, but you would essentially have to prepare a (test or estimated) return that you would not file with the software for the 2020 tax year. Doing so would require you to estimate the income and expenses for this tax year.
You can make estimate tax payments online or via EFTPS (after registration) - see links below.
Online: https://www.irs.gov/payments
EFPTS: https://www.eftps.com/eftps/
